Find angle D in the given diagram.

Based on the image provided, we have quadrilateral ABCD. We can observe that sides AB = AD and BC = CD, and angle ABC is given as 27°. Let's denote the angle DAB as x, which is the angle we want to find (angle D). Since AB = AD, triangle ABD is an isosceles triangle. Let's call the angle ADB (and also ABD) as y. Then, 2y + x = 180°. Since BC = CD, triangle BCD is also an isosceles triangle. Let's call the angle CDB (and also CBD) as z. Then, 2z + angle BCD = 180°. We know that angle ABC = angle ABD + angle CBD = y + z = 27°. The sum of all angles in a quadrilateral is 360°. Therefore, angle DAB + angle ABC + angle BCD + angle CDA = 360°, which translates to x + 27° + angle BCD + (y + z) = 360°. Since y + z = 27°, we have x + 27° + angle BCD + 27° = 360°. Thus x + angle BCD = 306°. Also, for triangle BCD, 2z + angle BCD = 180°. From y + z = 27°, we get z = 27° - y. Thus, angle BCD = 180° - 2z = 180° - 2(27° - y) = 180° - 54° + 2y = 126° + 2y. Now, we have x + angle BCD = x + 126° + 2y = 306°. We also know that 2y + x = 180°. From this, x = 180° - 2y. Substituting x in the previous equation, we have (180° - 2y) + 126° + 2y = 306°. Therefore, 306° = 306°, which does not help us to find the value of x. However, let's consider the given information carefully. AB = AD, and BC = CD. This means that ABCD is a kite. In a kite, the angles between the unequal sides are equal. Therefore, angle B = angle D. So, angle D = 27°. Answer: 27°